English

Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution

Statistical Mechanics 2009-10-31 v1

Abstract

We solve the Langevin dynamics of d-dimensional ferromagnetic spherical models with interactions that decay with distance as r^-(d+sigma). The long time dynamics of correlations and responses are studied in the different dynamical regimes and the validity of fluctuation-dissipation relations (or its violation) are shown. In particular, we show that the fluctuation-dissipation ratio X(t+t_w,t_w) is assymptotically a function only of the waiting time t_w in the aging regime and that X -> 0 as t_w -> oo . The results are valid in any finite dimension d and for 0 < sigma < 2, where short range behaviour is recovered. We also solve the T=0 Cahn-Hilliard dynamics of this model (conserved order parameter). An analysis of the multiscaling behaviour of the autocorrelation function is presented.

Keywords

Cite

@article{arxiv.cond-mat/0010319,
  title  = {Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution},
  author = {Sergio A. Cannas and Daniel A. Stariolo and Francisco A. Tamarit},
  journal= {arXiv preprint arXiv:cond-mat/0010319},
  year   = {2009}
}

Comments

10 pages, no figures

R2 v1 2026-07-22T10:09:48.265Z